The best blue cheese for this is salty but creamy, not too sharp or funky.
Using the tip of a paring knife, score an X in the bottom of each peach. Cook in a large saucepan of boiling water just until skins begin to peel back where cut, about 1 minute.
Using a slotted spoon, transfer to a bowl of ice water; let cool. Peel; cut over a small bowl into wedges, collecting juices. Add lemon juice and honey and toss to combine.
Toast bread, brush with 2 tablespoons oil, and season with salt. Spread cheese on toast and top with peaches, leaving juices behind. Whisk 4 tablespoons oil into juices. Toss purslane with enough dressing to lightly coat in a bowl; season with salt and pepper. Arrange over toasts.
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